Determine the values of a and b for which the line (a+2b−3)x (2a−b+1)y+6a+9=0 is parallel to x axis and y-intercept is −3. Also write the equation of the line. here is what i have tried.

Tiana Hill

Tiana Hill

Answered question

2022-09-27

Determine the values of a and b for which the line ( a + 2 b 3 ) x + ( 2 a b + 1 ) y + 6 a + 9 = 0 is parallel to x axis and y-intercept is 3. Also write the equation of the line.
here is what i have tried.
e q : ( a + 2 b 3 ) x + ( 2 a b + 1 ) y + 6 a + 9 = 0 Let the point be ( 0 , 3 )
Since the line is parallel to x axis therefore
slope of line = slope of x-axis
( a + 2 b 3 ) / ( 2 a b + 1 )
2 a b + 1 = 0
Now what?

Answer & Explanation

xgirlrogueim

xgirlrogueim

Beginner2022-09-28Added 13 answers

Since the equation ( a + 2 b 3 ) x + ( 2 a b + 1 ) y + ( 6 a + 9 ) .1 = 0 must represent the line 0. x + 1. y = 3.1, comparing the terms x , y , 1 in the equations, you must have
a + 2 b 3 = 0 , ( 2 a b + 1 ) / ( 6 a 9 ) = 1 / ( 3 ) .
Solving this system of equation you obtain a = 41 / 33 and b = 29 / 33.

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